Details

sample59.0ms

Algorithm

intervals

Results

22.0ms

256×

body

valid

simplify26.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
2	22	14
3	25	14
done	25	14

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.8b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`sqrt-prod`
11×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`sum-log`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`+-commutative` `rem-sqrt-square` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `associate-+l+` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

4 → 78

Calls

4 calls:

18.0ms	(+ (* x x) (* y y))
62.0ms	(+ (+ (* x x) (* y y)) (* z z))
168.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
62.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series563.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ (* x x) (* y y))
71.0ms	(+ (+ (* x x) (* y y)) (* z z))
98.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
333.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.5s

Counts

90 → 90

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	139	1707
1	367	1635
2	1899	1479
done	5001	1477

prune721.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
35.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite329.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`sqrt-prod`
17×	`*-un-lft-identity`
16×	`associate-r`
15×	`add-cube-cbrt`
13×	`times-frac`
11×	`add-log-exp`
9×	`pow1` `sqrt-div`
8×	`unswap-sqr`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`sum-log`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`+-commutative` `frac-times` `associate-*l/`
1×	`rem-sqrt-square` `associate-+l+` `sqrt-unprod` `associate-r/` `prod-exp` `-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 88

Calls

4 calls:

18.0ms	(+ (* x x) (* y y))
62.0ms	(+ (+ (* x x) (* y y)) (* z z))
175.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
66.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* x x) (* y y))
78.0ms	(+ (+ (* x x) (* y y)) (* z z))
327.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
199.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.8s

Counts

100 → 100

Iterations

Useful iterations: 2 (431.0ms)

Iter	Nodes	Cost
0	151	1959
1	395	1829
2	2062	1681
done	5001	1681

prune801.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
0.5b	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
35.7b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite572.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
75×	`times-frac` `sqrt-prod`
53×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`cbrt-prod`
25×	`associate-r`
16×	`unswap-sqr`
10×	`associate-l`
9×	`pow1` `add-log-exp`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r*`
5×	`sqrt-div`
4×	`div-inv`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `sum-log` `associate-/l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-times` `associate-+l+` `frac-2neg` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 157

Calls

4 calls:

62.0ms	(+ (+ (* x x) (* y y)) (* z z))
161.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
254.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
78.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series1.6s

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (+ (* x x) (* y y)) (* z z))
240.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
634.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
647.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify1.8s

Counts

169 → 169

Iterations

Useful iterations: 2 (457.0ms)

Iter	Nodes	Cost
0	223	4498
1	460	4310
2	2023	4070
done	5001	4070

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.2b

localize45.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow y 2) (pow z 2))
0.4b	(/ (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) (* (sqrt (cbrt 3.0)) (fabs (cbrt 3.0))))
35.7b	(sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2))))

rewrite432.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
18×	`sqrt-prod`
17×	`distribute-lft-out`
11×	`unpow-prod-down`
9×	`add-sqr-sqrt` `times-frac` `associate-/l*`
8×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`add-log-exp`
4×	`pow1` `sqrt-div`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `div-exp` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv`

Counts

3 → 66

Calls

3 calls:

29.0ms	(+ (pow y 2) (pow z 2))
237.0ms	(/ (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) (* (sqrt (cbrt 3.0)) (fabs (cbrt 3.0))))
162.0ms	(sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2))))

series1.2s

Counts

3 → 9

Calls

3 calls:

53.0ms	(+ (pow y 2) (pow z 2))
1.0s	(/ (sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2)))) (* (sqrt (cbrt 3.0)) (fabs (cbrt 3.0))))
180.0ms	(sqrt (+ (pow x 2) (+ (pow y 2) (pow z 2))))

simplify1.1s

Counts

75 → 75

Iterations

Useful iterations: 2 (292.0ms)

Iter	Nodes	Cost
0	117	1531
1	285	1375
2	1149	1283
done	5000	1283

prune664.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 16.2b

regimes1.9s

Accuracy

61.7% (7.5b remaining)

Error of 26.0b against oracle of 18.4b and baseline of 38.1b

bsearch348.0ms

Steps

Iters	Range		Point
9	6.578703183529628e+91	1.1448241580470724e+99	1.119152176003768e+99
10	-7.556856097197653e-296	2.9792793194115403e-307	-1.7754786637459033e-299
9	-1.1739783025602866e-268	-1.5231580497035754e-273	-1.5378615096700336e-273
8	-1.4374651696982963e+145	-2.0346029743301018e+142	-3.983694464815315e+143

simplify47.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	75
1	54	75
2	60	75
3	61	75
done	61	75

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.3s

8000×

body

valid